analysis of edge detection technique for hardware...

Nidhi Panda

Department of Electrical EngineeringNational Institute of Technology Rourkela

Analysis of edge detection technique forhardware realization

Analysis of edge detection technique for hardwarerealization

Dissertation submitted to the

National Institute of Technology Rourkela

in partial fulfillment of the requirements

of the degree of

Master of Technology

in

Electrical Engineeringin specialization

Electronic System and Communication

by

Nidhi Panda(Roll No: 214EE1411)

under the supervision ofProf. Supratim Gupta

Department of Electrical Engineering,National Institute of Technology, Rourkela,

Rourkela-769008, Orissa, India2014-2016

Electrical EngineeringNational Institute of Technology Rourkela

Dr. Supratim GuptaAssistant Professor

May 31, 2016

Supervisor’s Certificate

This is to certify that the work presented in this dissertation entitled“ Analysis ofedge detection technique for hardware realization” by “Nidhi Panda”, Roll Number214EE1411, is a record of original research carried out by her under my supervisionand guidance in partial fulfillment of the requirements of the degree of Master ofTechnology in Electrical Engineering. Neither this dissertation nor any part of it hasbeen submitted for any degree or diploma to any institute or university in India orabroad.

<Supervisor’s Signature><Supratim Gupta>

Declaration of Originality

I, Nidhi Panda , Roll Number 214EE1411 hereby declare that this dissertationentitled “ Analysis of edge detection technique for hardware realization”represents my original work carried out as a postgraduate student of NIT Rourkelaand, to the best of my knowledge, it contains no material previously published orwritten by another person, nor any material presented for the award of any otherdegree or diploma of NIT Rourkela or any other institution. Any contribution madeto this research by others, with whom I have worked at NIT Rourkela or elsewhere,is explicitly acknowledged in the dissertation. Works of other authors cited in thisdissertation have been duly acknowledged under the section “Bibliography”. I havealso submitted my original research records to the scrutiny committee for evaluationof my dissertation.

May 31, 2016NIT Rourkela

Nidhi Panda

Dedicated to My Grand Mother.

Acknowledgements

First and foremost, I am truly indebted to my supervisor Profes-

sor Supratim Gupta for his inspiration, excellent guidance and unwavering

confidence through my study, without which this thesis would not be in its

present form. From the bottom of my heart, I would like to express my grati-

tude to Dr. Supratim Gupta for all the support, patience and encouragement

throughout the work.

I thank Mr. Susant Panigrahi and Mr. M.Zefree Lazarus for the stimu-

lating discussions, knowledge sharing sessions, and all the support that they

have given me during this work.

I would like to thank my fellow lab mates Kiran Patel, Amrita Maity and

Suparna Rooj of Embedded System and Real Time Lab and all my M.Tech

and dual degree friends of NIT Rourkela, for their enjoyable and helpful

company I had with.

I thank Mr. Sreejith M, former student of ESRT lab NIT, Rourkela from

IIT Kharagpur for the help and support that he gave me to learn image

processing in VHDL.

My wholehearted gratitude to my parents, Devendra and Madhu Panda,

my aunty Sudha Panda and sisters Aparna and Ranu Panda, for their en-

couragement and support.

Nidhi Panda

Rourkela, May 2016

v

Abstract

Edge detection plays an important role in image processing and computer

vision applications. Different edge detection technique with distinct criteria

have been proposed in various literatures. Thus an evaluation of different

edge detection techniques is essential to measure their effectiveness over a

wide range of natural images with varying applications. Several performance

indices for quantitative evaluation of edge detectors may be found in the liter-

ature among which Edge Mis-Match error (EMM), F-Measure (FM), Figure

of Merit (FOM) and Precision and Recall (PR) curve are most effective.

Several experiments on different database containing a wide range of natural

and synthetic images illustrate the effectiveness of Canny edge detector over

other detectors for varying conditions. Moreover, due to the ever increasing

demand for high speed and time critical tasks in many image processing ap-

plication, we have implemented an efficient hardware architecture for Canny

edge detector in VHDL. The studied implementation technique adopts par-

allel architecture of Field Programmable Gate Array (FPGA) to accelerate

the process of edge detection via. Canny’s algorithm. In this dissertation, we

have simulated the considered architecture in Modelsim 10.4a student edition

to demonstrate the potential of parallel processing for edge detection. This

analysis and implementation may encourage and serve as a basis building

block for several complex computer vision applications. With the advent of

Field Programmable Gate Arrays (FPGA), massively parallel architectures

vii

can be developed to accelerate the execution speed of several image pro-

cessing algorithms. In this work, such a parallel architecture is proposed to

accelerate the Canny edge detection algorithm. The architecture is simulated

in Modelsim 10.4a student edition platform. This work has wider scope and

applications. FPGA based edge detection system can serve as the basic step

for implementations of complex computer vision algorithms.

Keywords: Consensus Ground Truth, Edge Mismatch Error (EMM), F-

Measure (FM), Figure of Merit (FOM), FPGA, Precision Recall (PR) curve,

VHDL Architecture.

Contents

Contents i

List of Figures vi

List of Tables viii

1 Introduction 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Comparative analysis of different edge detection techniques 2

1.2.2 Hardware Image Processing . . . . . . . . . . . . . . . . . 3

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Edge Detection Methodologies 6

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Classical method . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Roberts operator . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Sobel operator . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3 Prewitt operator . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Phase Based method . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Gaussian based method . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.1 LOG operator . . . . . . . . . . . . . . . . . . . . . . . . . 13

i

CONTENTS ii

2.4.2 Canny’s operator . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6 Gradient Calculation . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7 Non Maxima Suppression . . . . . . . . . . . . . . . . . . . . . . 18

2.8 Hysteresis Thresholding . . . . . . . . . . . . . . . . . . . . . . 20

2.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Performance Evaluation 22

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Ground Truth Generation . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Artificial approach . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2 Real and Manually annotated approach . . . . . . . . . . . 23

3.2.3 Consensus approach . . . . . . . . . . . . . . . . . . . . . 24

3.2.4 Minimean Method . . . . . . . . . . . . . . . . . . . . . . 25

3.2.5 MiniMax method . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Performance measures . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Edge Missmatch Error (EMM) . . . . . . . . . . . . . . . 28

3.3.2 figure Of Merit(FOM) . . . . . . . . . . . . . . . . . . . . 29

3.3.3 F-measure . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.4 Precision Recall (PR)Curve . . . . . . . . . . . . . . . . . 30

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Real-time Canny Edge Detection System Design 32

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Architecture Selection/Parallel Algorithm Development . . . . . 32

4.2.1 Architecture Selection on FPGA . . . . . . . . . . . . . . . 32

4.2.2 FPGA Computational Architecture Selection . . . . . . . . 33

4.2.3 Selection of FPGA Mapping Techniques . . . . . . . . . . 33

4.3 Over all architecture . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3.1 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

CONTENTS iii

4.3.2 Gradient and magnitude calculation . . . . . . . . . . . . . 35

4.3.3 Non-maxima calculation . . . . . . . . . . . . . . . . . . . 37

4.3.4 Hysteresis calculation . . . . . . . . . . . . . . . . . . . . . 38

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Design of a VHDL Test-bench for Canny edge detection 40

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 Need for the Test-Bench . . . . . . . . . . . . . . . . . . . . . . 40

5.3 Model for an Image Processing System . . . . . . . . . . . . . . 41

5.4 Image Representation . . . . . . . . . . . . . . . . . . . . . . . . 41

5.5 Image Processing Test Bench . . . . . . . . . . . . . . . . . . . . 42

5.5.1 Image to Hex-Image Converter . . . . . . . . . . . . . . . 43

5.5.2 VHDL Camera Module . . . . . . . . . . . . . . . . . . . . 44

5.5.3 Output Display Module . . . . . . . . . . . . . . . . . . . 44

5.5.4 Output Signals from Test Bench . . . . . . . . . . . . . . . 45

5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6 Results and Discussion 48

6.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.1.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . 48

6.1.2 Consensus based reference image generation . . . . . . . . 49

6.1.3 Performance measure on different data base . . . . . . . . 49

6.1.4 Precision Recall curve . . . . . . . . . . . . . . . . . . . . 52

6.1.5 Edge detection in VHDL . . . . . . . . . . . . . . . . . . . 53

6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7 Conclusion and Future Work 57

7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Bibliography 59

List of Abbreviations

Abbreviation Description

1D One Dimension

2D Two Dimension

CE Common Edges

EMM Edge Miss Match Error

EO Excess edges

ET Excess Thresholded Edge

FN False negative

FOM Figure of merit

FP False positive

FPGA Field Programmable Gate Array

FPR False positive rate

PC Phase Congruency

PR curve Precision recall curve

TN True negative

TP True positive

TPR True positive rate

VHDL Very High Speed Integrated Circuit (VHSIC) Hardware De-

scription Language

iv

List Symbols

Symbols Description

x, y Spatial coordinates

f Frequency

d Dimension

Z Complex Plane

φ Phase

m Magnitude

N Length of Time Series

δ Distance function

r, θ Polar Co-ordinates

μ Mean

σ Standard Deviation

I(x, y) Image

c Contrast

S(x, y) Smoothed image

G(x, y) Filter mask

v

List of Figures

2.1 Roberts mask along x and y direction . . . . . . . . . . . . . . . . 8

2.2 Input and output image for Roberts mask . . . . . . . . . . . . . . 9

2.3 Sobel mask along x and y direction . . . . . . . . . . . . . . . . . . 9

2.4 Input and output image for Roberts mask . . . . . . . . . . . . . . 9

2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Input and output image for Prewitt mask . . . . . . . . . . . . . . 10

2.7 Input and output image for . . . . . . . . . . . . . . . . . . . . . . 13

2.8 Input and output image for LOG operator . . . . . . . . . . . . . . 15

2.9 Input and output image for Zero-crossing . . . . . . . . . . . . . . 15

2.10Gaussian mask and smoothed image after masking . . . . . . . . . 17

2.11Gradient magnitude image . . . . . . . . . . . . . . . . . . . . . . 18

2.12The angle approximation of edge normals in four predefined angles 19

2.13Image after nonmaxima suppression . . . . . . . . . . . . . . . . . 19

2.14Edge image after Hysteresis thresholding . . . . . . . . . . . . . . . 20

3.1 frame work for generation of consensus ground truth . . . . . . . . 27

3.2 Input image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Consensus ground truth image generation . . . . . . . . . . . . . . 28

3.4 Confusion matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1 Architecture for Gaussian smoothing . . . . . . . . . . . . . . . . . 35

vi

LIST OF FIGURES vii

4.2 Buffering operation . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3 Buffering operation . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 Indexing Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.5 Data flow of pipeline in first three clock . . . . . . . . . . . . . . . 37

4.6 Data flow of pipeline in next two clock . . . . . . . . . . . . . . . . 37

4.7 Gradient and magnitude calculation . . . . . . . . . . . . . . . . . 37

4.8 Non maxima calculation . . . . . . . . . . . . . . . . . . . . . . . . 38

4.9 Hysteresis calculation . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.1 Model of Image Processing System . . . . . . . . . . . . . . . . . . 41

5.2 Image Representation in analog form . . . . . . . . . . . . . . . . . 42

5.3 Image Representation in digital form . . . . . . . . . . . . . . . . . 42

5.4 Block diagram of a image processing test bench . . . . . . . . . . . 43

5.5 Coding of image into a hex image file . . . . . . . . . . . . . . . . 44

5.6 Algorithm for generating composite image signal from hex file . . . 45

5.7 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.1 Consensus based reference image using . . . . . . . . . . . . . . . . 50

6.2 MATLAB based GUI for edge detection evaluation. . . . . . . . . 50

6.3 Comparison of detectors for minimean method using PR curve . . 53

6.4 Comparison of detectors for minimax method using PR curve . . . 54

6.5 Input image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.6 Sobel edge detector MATLAB and VHDL output . . . . . . . . . . 55

List of Tables

6.1 Database used for experimental validation . . . . . . . . . . . . . . 49

6.2 Performance measure for Caltech airplane database with minimean 50

6.3 Performance measure for Caltech leaves datasbase with minimean 51

6.4 Performance measure for TID2008 with minimean . . . . . . . . . 51

6.5 Performance measure for Zurich Object Database with minimean . 51

6.6 Performance measure for Caltech airplane datasbase with minimax 51

6.7 Performance measure for Zurich Object Database with minimax . 51

6.8 Performance measure for Caltech leaves database with minimax . 52

6.9 Performance measure for TID2008 database with minimax . . . . 52

6.10AUC calculation for Precision Recall curve using minimean method 52

6.11AUC calculation for Precision Recall curve using minimax method 55

viii

Chapter 1

Introduction

1.1 Introduction

Edge detection in an image is the fundamental tool in computer vision and

image processing for the identification and reconstruction of local properties.

In an image most of its shape and structural information is included in edge.

So in image identification process, initially edges are detected, while removing

less important redundant information. This process aides in retaining objects

and shape information of an image with increasing sharpness. However, most

of the natural images may be acquired in different conditions with varying

properties such as difference in illumination condition, depth discontinuity

etc. Thus the process of identifying edges considering a generalized method-

ology is a challenging task. Most of the edge detector differs in mathematical

and algorithmic property. The comparative study of various edge detection

techniques is essential to have an understanding on all edge detector. Though

several matrices [1] may be found in the literature for comparative analysis,

most of these indices measure the performance of edge detectors with respect

to reference edge map. In this dissertation, we have considered consensus [2]

of different edge map to generate ground truth image.

Traditional image processing algorithms are sequential in nature. When

1

CHAPTER 1. INTRODUCTION 2

these algorithms are implemented in a real-time system, the response time

will be high. In an embedded platform, such algorithms consumes more power

because of more number of clock cycles required to execute the algorithm.

With the advent of Field Programmable Gate Arrays (FPGA), massively

parallel architectures can be developed to accelerate the execution speed of

several image processing algorithms. In this work, such a parallel architecture

is studied to accelerate the Canny edge detection algorithm. The architecture

is simulated in Modelsim 10.4a student edition platform. FPGA based edge

detection system can serve as the basic step for implementations of complex

computer vision algorithms. Such as in fast face detection in a digital camera,

fast object tracking, policing and interactive surveillance and object tracking

[3].

1.2 Motivation

1.2.1 Comparative analysis of different edge detection techniques

The estimation of edge in different detectors vary distinctively according to

the choice of smoothing filter, the differential operator, and the localiza-

tion method. Furthermore, few external factors such as: change in contrast,

inadequate illumination, image magnification and blurring may affect edge

localization and detection in various detectors. Thus an evaluation of differ-

ent edge detection techniques is essential to measure their effectiveness over a

wide range of natural images with varying applications. Several performance

indices may be found in the literature for quantitative evaluation of different

edge detection methodologies. However, most of the performance indices are

evaluated with respect to the ground truth edge map. In image processing

applications the reference image generation can be categorized broadly into

three approaches.

• Artificial approach


• Real and Manually annotated approach

• Consensus approach

Artificial approaches are simplest. However many natural images contain

objects with different textural characteristic, various percentage of homoge-

nous regions and details, that may not be analyzed using this approach. The

second approach is real and manually annotated approach, since the reference

edge map generated in this approach relies on human observer, it is neither

automatic nor efficient (both in terms of accuracy and time complexity).

Furthermore, different subject annotate different pixel position to generate

several reference edge map for same image. Thus this approach also have

limited applications in edge detection performance evaluation. The need for

automatic, accurate and time efficient method for reference image generation

motivates many researcher in last few decades. The consensus approach is

one such algorithm(s) (with different parameter values) used for ground truth

edge map generation.

1.2.2 Hardware Image Processing

A microcontroller/dsp processor executes algorithms sequences sequentially.

If multiple hardware circuits can be designed to carry out different algorithm

sequences in parallel, there will be considerable increase in overall execution

speed. Suppose a system has to be designed such that the brightness of the

incoming frames has to be increased. Brightness of an image can be increased

by multiplying each pixel gray level with a constant α, and then adding a

gain constant β to it as in equation

g(i, j) = f(i, j)× α + β (1.1)

In a typical microcontroller/dsp processor based design, this will involve

storing the frames in a buffer, and then performing the operations mentioned


in Eq. 1.1 to each pixel gray level, in a loop. Suppose each addition instruc-

tion takes 12 clock cycle, and each multiplication instruction takes 36 clock

cycle, then total number of clock cycles required to process one pixel will be

48. If the incoming frames are of size 100× 100, then such a design will need

100× 100× 48 clock cycles to process the entire frame. Now suppose, there

are 10000 adder and multiplier circuits, one cosponsoring to each pixel. In

such a design, all the pixels can be processed in parallel. Thus total operation

can be implemented in just two clock cycles. In principle, such a system will

be 12000 times faster than system based on sequential processor. In actual

designs, algorithm will be divided in to parallel blocks and will be executed

simultaneously. In a nutshell, the significant increase in processing speed is

the major motivation behind hardware image processing. If the processing

time is less, the power consumption can also be reduced. Hence it can be

observed that the parallel processor based hardware implementation of image

processing systems aid better performance in time critical applications. In

the current scenario, most of the image processing algorithms are running in

a sequential environment. Here, we have investigated on a architecture for

FPGA based edge detection technique, which may have grater significance

and scope in time critical applications.

1.3 Objectives

The salient objectives of the thesis are:

i. Comparison of various edge detection technique.

a) Automatic generation of ground truth edge map using consensus of

various edge detectors.

b) Quantitative performance evaluation of considered edge detectors

adopting four different measures: EMM, FOM, F-Measure and PR

curve.


ii. Hardware architecture development and implementation of best edge de-

tector in FPGA.

1.4 Thesis Organization

The rest of the thesis is organized as follows: Chapter 2 classifies different

edge detection techniques and discusses each detection algorithm in detail.

Chapter 3 measures the performance of reported edge detection technique

with respect to a reference edge map generated from the consensus of each

method. The design of VHDL test bench for edge detection is studied in

chapter 4. Chapter 5 elaborates about architecture of Canny edge detection

algorithm in VHDL. The simulation results for edge detection techniques both

in VHDL and MATLAB are presented and discussed in chapter 6. Chapter

7 concludes and provides future scope of this thesis.

Chapter 2

Edge Detection Methodologies

2.1 Introduction

In many image and computer vision applications, it is required to capture

the distinct properties of objects in an image. These properties may be char-

acterize by the photometrical, geometrical and physical phenomenon of the

object, which can be distinguished in local maxima, discontinuity (step edges)

and junctions [4]. The edge detection techniques are adapted to localize and

identify these physical phenomena of the image. In ideal situation, the result

of edge detector to any image covers all the discontinuities. However, as it

has been proven that discontinuities in intensity corresponds to the change

in depth, surface orientation, material properties and illumination. It is al-

most impossible to get to capture and localize these edges, precisely. Thus

different type of edge detectors [5] are used for specific applications.

In most of the detectors the process of detecting edges may be divided into

the following three steps.Assuming image is corrupted with additive Gaussian

noise, in the first step image is smoothen using low pass filter. This step not

only reduces the noise but also suppresses the edges. Thus a trade off between

smoothing and edge preservation is essential. The second step is a process of

finding edges by using high pass filters. Assuming image is corrupted with

6

CHAPTER 2. EDGE DETECTION METHODOLOGIES 7

additive Gaussian noise, in the first step image is smoothen using low pass

filter. This step not only reduces the noise but also suppresses the edges.

Thus a trade off between smoothing and edge preservation is essential.

1. Classical method

• Roberts Operator

• Sobel Operator

• Prewitts operator

2. Phase based method

• Phase Congruency

3. Gaussian based method

• LOG operator

• Zero crossing detector

• Canny’s edge detector

2.2 Classical method

Popular edge detection methods which falls in this categories are Roberts [6],

Sobel[7], Prewitt[7] and Kritch operator[7]. In this search based approach,

initially a first order derivative based mask is used to compute the gradient

magnitude to measure edge strength (as shown in Eq.2.2). Then the orienta-

tion of edges are estimated using Eq.2.2 for gradient direction. Though this

approach is computationally inexpensive, it is highly sensitive to noise in lack

of filtering/smoothing.

M(i, j) =√

G2x +G2

y (2.1)

θ(i, j) = tan [Gy

Gx] (2.2)


Here,

� Gx = Gradient in x-direction

� Gy = Gradient in y-direction

� M(i,j) = Edge strength

� θ = Edge direction

To get an approximation of edges only magnitude will be enough. There-

fore we use thresholding to find the edges in the gradient image for classical

approach.

2.2.1 Roberts operator

This operator was proposed by Lawrence Roberts in 1963[6]. The esse of

Roberts work is to use discrete differentiation to find the gradient of the

image. This can be done by using a 2× 2 mask as shown in figure 2.1a and

2.1b.

(a) (b)

Figure 2.1: Roberts Mask ,(a) x direction, (b) y direction

As this operator is using 2x2 mask it is computationally very simple but

it lacks in efficiency of edge detection.

2.2.2 Sobel operator

It is the most popular edge detector in classical edge detectors. It is proposed

by Irwin Sobel & Gary Feldman in 1970 [8]. It uses 3x3 convolution mask in

horizontal and vertical direction to find the gradient. The masks as shown in

figure 2.3a and 2.3b (known as Sobel’s mask) not only computes the gradient


(a) (b)

Figure 2.2: Roberts Mask , (a) input image, (b) edge image

in both X and Y directions but also provides an extra weighting factor of 2,

that smoothens the image and reduces noise.

(a) (b)

Figure 2.3: Sobel Mask, (a) x direction, (b) y direction

(a) (b)

Figure 2.4: Sobel Mask, (a) input image, (b) edge image

This mask is combination of both averaging and differentiation operation,


which makes it more immune to noise than Robert’s operator. The advantage

of Sobel mask is that, it is very simple and the coefficients values and kernel

size can be changed according to requirement. The edges of image after

Sobel are thick so they can not be used where the peripheral contour is area

of interest.

2.2.3 Prewitt operator

This operator was given by Judith M. S. Prewitt in 1970. It also uses a

3x3 mask with only values 0, 1, & -1. Prewitt Operator compute the edges

by using the mask as shown in figure 2.5a and 2.5b. The result of prewitt

operator is as shown in figure 2.6b.

(a) Prewittmask alongx and y di-rection

(b)

Figure 2.5: Prewitt Mask , (a) x direction, (b) y direction

(a) (b)

Figure 2.6: Prewitt Mask , (a) input image, (b) edge image

The result of Prewitt operator is shown in figure 2.6b. As this mask does


not give extra weight to center pixel value it is more sensitive to noise then

Sobel mask. Also the mask coefficient and the kernel size are fixed for this

type of operator.

2.3 Phase Based method

A clear idea about feature can be extracted at any angle by Congruency of

phases. Angle at which congruency occurs suggest the edge type, i.e step or

delta. Morrone et al.[9] and Morrone and Owens developed a Local Energy

Model. Other work in this modelling of edges can be model of feature percep-

tion can be obtained in Morrone and Burr , Owens et al.[10], Venkatesh and

Owens , and Kovesi [11]. Morrone and Burr [9] showed that this modelling

clearly shows psychophysical effects in edge perception.

The phase congruency measure given by Morrone et al. [9] is

PC1(z) =|E(z)|∑nAn(z)

(2.3)

here,

� |E(z)| = Local energy

� An(z) = Amplitude of Fourier component at location x.

Therefore, phase congruency (PC) can be defined as ratio of |E(z)| to the

complete path length used by the local Fourier components till the end point.

Here, the ratio of |E(z)| to the An(z) will be 1, only if all Fourier components

will be phase, i.e all complex vectors will be aligned. And the ratio will be

zero if no coherence in phases occur. Phase Congruency Methods are better

than methods which are gradient based.As the gradient based methods are

easily effected by blurring, illumination condition and magnification. PC is

a limitless quantity which does not vary whit environmental condition. This


PC measure is a function of cosine of the deviation of each phase component

from the mean value. This can be expressed as shown in Eq. 2.4.

PC1(z) =

∑nAn(cos(φ(z)− φ(z)))∑

nAn(z)(2.4)

This phase congruency measure does not provide good localization and

are also not robust to noise. Pater Kovesi [11] developed a modified measure

of Phase congruency which provide more localization and also less sensitive

to noise but the problem with it is computationally very intensive. This

Modified Measure of Phase congruency is as shown in Eq.2.5.

PC(z) =W (z)�E(z)− T �∑

nAn(z) + ε(2.5)

� T = Threshold

� W(z) = Weighting function

� ε = Small positive constant

� E(z) =√F (z)2 +H(z)2

This can also be represented as cosine minus the magnitude of the sine of the

phase deviation as shown in Eq. 2.6.

PC2(z) =W (z)�An(z)(cos(φ(z)− φ(z)))− | sin(φ(z)− φ(z))| − T �∑

nAn(z) + ε(2.6)

2.4 Gaussian based method

In many image processing applications Gaussian based methods for feature

extraction are highly appreciated and utilized for edge detection. It has

been proven that these filters play a major role in the fields of biological

vision specifically for the human-vision systems. Gaussian filter-based edge

detection techniques are developed on the basis of physiological examinations


(a) (b)

Figure 2.7: Phase congruency, (a) input image, (b) edge image

and prominent properties of the Gaussian function which enables to execute

edge detection analysis.

2.4.1 LOG operator

The Gaussian based approach for edge detection was first proposed By Marr

and Hildreth [12]. The intensity variation in an image occurs at different level

is considered for feature extraction. Thus a smoothing filter at each scale is

adopted to serve the purpose. As at different scales a single filter may not

be optimum, Marr and Hildreth suggested 2D Gaussian function which can

be defined in Eq. 2.7.

G(x, y) =1

2πσ2exp

−(x2+y2)

2σ2 (2.7)

where

� σ = Standard deviation

� (x, y) = Pixel’s cartesian coordinates

As it is already proven that the Gaussian filters produce different set of

image with distinct level of smoothing, a zero crossing of second derivative

of Gaussian to find the edges. Such a second order derivative based scalar


approximated filter as in Eq. 2.8 known as Laplacian of Gaussian (LOG) is

considered Eq. 2.8 for edge computation.

g(x, y) = ∇2[G(x, y) ∗ I(x, y)] (2.8)

where

� ∇= Laplacian operator

� g(x,y) = Image after Laplacian

� G(x,y) = Smoothed image

� I(x,y)=Input image

LOG is an orientation independent filter. It breaks down at curves, cor-

ners and on the locations where intensity value varies nonlinearly along the

edges. Thus this operator has limitation in detecting edges at these loca-

tions. According to Marr and Hildreth, we can implement smoothing and

differentiation just by using the Laplacian of Gaussian function. The LOG

with scale σ is as in Eq.2.8.

fσ(x, y) = ∇2G(x, y) = [x2 + y2 − 2σ2

σ4] exp

−(x2+y2)

2σ2 (2.9)

The Marr-Hildreth algorithm for edge detection can be wrap-up in follow-

ing points

• Smoothing of image by using Gaussian filter obtained by Eq. 2.7.

• Calculation of Laplacian on the image by using Eq. 2.8

• Search for zero crossing in image

2.4.2 Canny’s operator

Canny’s approach for edge detection is based on three basic criteria [13].


(a) (b)

Figure 2.8: LOG, (a) input image, (b) edge image

(a) (b)

Figure 2.9: Zero-crossing, (a) input image, (b) edge image

1. Good detection - The probability of the detection of the true edge

points must be high enough.

2. Good Localization - The edge points must be well localized i.e. they

must be nearer to the true edge point.

3. Single edge response- There must be only one response to the single

edge.

The esse of canny’s work is to proof these criteria mathematically and

finding an optimal solution to it. It is almost impossible to satisfy all these


objectives. Therefore numerical optimization is used with 1D step edges, with

additive white Gaussian noise. It is observed that first derivative of Gaussian

gives good approximation. But 1D approximation is applied to the direction

of the edge normal which is unknown beforehand. Thus the following steps

is suggested for better approximation.

• Smoothing - A 2D filtering is used for smoothing and noise reduction.

• Gradient calculation - Any edge detection mask can be used to find the

horizontal and vertical gradient.

• Non-Maximum suppression - Suppress the non edge pixel and increases

localization.

• Hysteresis thresholding - It removes the false edges by using two thresh-

old value.

An overview of Canny’s edge detection framework is shown in Fig.fig:ch2:

Canny Edge detector, which utilizes all mentioned steps for feature extrac-

tion.

2.5 Smoothing

Smoothing is the first step of Canny edge detector. Image acquisition, limits

of digital system and ambient conditions corrupts the image. Generally the

noise, observed in images is Gaussian and additive in nature. So smoothing

is essential. For smoothing Gaussian mask is used. As literature suggests

that volume under the 2D Gaussian surface, between ±3σ about the mean

is 99.7%. Therefore the size of n × n Gaussian filter should be greater than

or equal to 6σ. The 2D Gaussian function is given in Eq.2.11. Gaussian

mask suppresses the high frequency components. As noise is high frequency

component it minimizes noise but also causes loss of information [5]. In image


processing we stabiles a tradeoff between noise reduction and preservation of

edge information.

G(x, y) = exp−(x2+y2)

2σ2 (2.10)

If input image is I(x, y) and smoothed image is S(x, y) then, after Gaussian

the smoothed image is

S(x, y) = G(x, y) ∗ I(x, y) (2.11)

Here we use a 3× 3 window with sigma equals to 0.5.

(a) (b)

Figure 2.10: Smoothing operation, (a) Gaussian Mask of 3× 3,(b) Smoothed image

2.6 Gradient Calculation

The first order differentiation operator, similar to Sobel’s mask in figure 2.3a

and 2.3b is used for the computation of gradient in horizontal and vertical

direction as formulated in Eq.2.12 and equ:ch4:Gradient Calculation in y.

These are used to find the magnitude i.e. edge strength as in Eq. 2.14 and

direction as in Eq. 2.15 at every pixel position. Gradient magnitude can

be calculated either by Euclidean distance measure by applying Pythagoras

theorem or by using Manhattan distance measure. Manhattan distance mea-

sure is an approximation method for reducing the computation complexity.


Image gradient provides an estimation about the edges, however as shown

in figure 2.13a the edges in the image are not properly localized. Thus we

find the gradient direction which can be used in the suppression of local edge

points in the non maximum suppression.

δS

δx= S(i, j) ∗G(i, j) (2.12)

δS

δy= S(i, j) ∗G(i, j) (2.13)

M(i, j) =

√δS

δx+

δS

δy(2.14)

θ(i, j) = tan [

δSδy

δSδx

] (2.15)

(a)

Figure 2.11: Gradient magnitude image

2.7 Non Maxima Suppression

In this step it scan the gradient magnitude image along the edge direction.

If the pixel values does not belongs to local maxima we mark it as no edge

point. Thus we suppress all edge point which are not the part of local maxima.


Therefore, the process of non maxima suppression is also known as thining

process. The steps for the calculation of non maxima suppression is as follows.

1. Round off the gradient direction into 4 direction as shown in figure 2.12.

2. Compare the current pixel with its two neighborhood along the direction.

3. If the magnitude of the current pixel is less than any of the magnitude

of its neighbor along the direction replace the current pixel with zero i.e.

no edge. Else the current pixel is marked as edge point.

Figure 2.12: The angle approximation of edge normals in four predefined angles

(a)

Figure 2.13: Image after nonmaxima suppression


(a)

Figure 2.14: Edge image after Hysteresis thresholding

2.8 Hysteresis Thresholding

The image we get after non-maxima suppression may have number of false

edge which are observed due to the high frequency components of noise. The

easiest way to remove this is thresholding. Thresholding is the simplest way

to suppress both false and noisy edges. Thus a better localization is achieved

by using two thresholds, which excels in following ways:

1. Detects strong edges that are having strength greater than high threshold

value.

2. Detects weak edge pixels which are having strength in between high and

low threshold value.

3. Suppresses edge pixels which are having edge strength less than lower

threshold value. We suppress these pixels.

As Canny’s algorithm includes smoothing, non maxima suppression and

hysteresis for noise removal, localization and false edge removal respectively.

It provides better detection, localization, and single point response. The

demerit of this detector is its time complexity.


2.9 Discussion

In this chapter we revisited and discussed on different types of edge detection

algorithm in brief. The results thus obtained from all the methods indicate

that the performance of different edge detectors vary distinctively. Therefore

comparison on different edge detector is essential.

Chapter 3

Performance Evaluation

3.1 Introduction

As discussed in previous Chapter 2, the estimation of edge in different de-

tectors vary distinctively according to the choice of smoothing filter, the dif-

ferential operator, and the localization method. Furthermore, few external

factors such as: change in contrast, inadequate illumination, image magni-

fication and blurring may affect edge localization and detection in various

detectors. Thus an evaluation of different edge detection techniques is essen-

tial to measure their effectiveness over a wide range of natural images with

varying applications. Several performance indices such as: Edge miss match

error (EMM)[1], F-measure[1], figure of merit (FOM)[1] and Precision recall

(PR) curve [14] may be found in the literature for quantitative evaluation of

different edge detection methodologies. However, most of the performance

indices are evaluated with respect to the ground truth edge map (structure)

[2]. In this chapter along with different quantitative metrics, we will also

discuss various methods of reference image generations both via. manually

(by visual inspection) and automatically.

22

CHAPTER 3. PERFORMANCE EVALUATION 23

3.2 Ground Truth Generation

Quantitative comparison of different edge detection technique needs the use

of performance measures. These measure need a reliable ground truth or

reference image for evaluation. In image processing applications for edge de-

tection the process of generation of reference image may be classified broadly

into three

• Artificial approach

• Real and Manually annotated approach

• Consensus approach

3.2.1 Artificial approach

This is the simplest way of generation of the ground truth image. Artificial

approaches are only limited in generating reference image for synthetic im-

age. However many natural images contain objects with different textural

characteristic, various percentage of homogenous regions and details, that

may not be analyzed using this approach. Thus most of the researchers do

not consider results based on synthetic images as convincing and still wish

to see results on natural images.

3.2.2 Real and Manually annotated approach

In this approach the natural images are examined manually and edges in the

image are marked by the experts in the field. Since the reference edge map

generated in this approach relies on human observer, it is neither automatic

nor efficient (both in terms of accuracy and time complexity). Furthermore,

different subject annotate different pixel position to generate several reference

edge map for same image. It is also possible that the same annotator can use

different criteria for the generation of different reference images from a single

image. Owing to these difficulties the quantitative measure is generally done


by using synthetic images. Thus this approach also have limited applications

in edge detection performance evaluation.

3.2.3 Consensus approach

The need for automatic, accurate and time efficient method for reference im-

age generation motivates many researcher in last few decades. The consensus

approach is one such algorithm(s) (with different parameter values) used for

ground truth edge map generation [2, 15, 16]. These ground truth images are

easy to generate and could be used for performance evaluation. Bryant and

Bouldin [15] have compared six edge detectors with relative grading method.

They have used True positive (TP) and True negative (TN) statistics along

with consensus by using following agreement criterion, is considered for ref-

erence edge generation. Any point will be a part of ground truth if minimum

K number of edge detector will detect it. Where 1 ≤ K ≤ N , if N is total

number of edge detector. However, the choice of K is biased and it penalizes

those algorithms, that didn’t agree with other algorithms [16]. To overcome

this [2] proposed a method in which the selection of K is optimized and au-

tomated. In this approach each detector each proposed method search for

all levels of consensus and the most appropriate is selected. Thus, the effect

of the failings of the some algorithms does not affect with the higher level of

consensus selection. In the earlier method Yitzhaky and Peli [17] proposed

an evaluation technique of edge detectors which uses a statistical objective

performance analysis and the detector’s parameter selection by using con-

sensus method. This algorithm may be used to compare output of different

edge detector binary format. [2] have also considered the same assumption

for reference image creation. For the comparison of different edge detectors

it is not necessary to have an accurate, reliable and automatic algorithm for

reference binary edge map generation. This framework, initially uses differ-

ent edge detectors to generate various consensus ground truth images using


a voting technique [2]. Then the optimum consensus level K is selected us-

ing minimean and minimax approach from various Baddeley measures [18].

Here, we have considered all the discussed edge detectors in Chapter 2 for

automatic reference image generation using consensus method. The block

diagram for this framework is shown in figure 3.1 and each step of this algo-

rithm is discussed as follows:

1. N different edge detectors are applied.on any natural image to find N

different edge maps (outputs Oj) as Oj, jε{1, 2, . . . , N}.2. These N output images are used to generate different consensus images

Ck such as Ck is consisting of edge pixel which as defined as edge point

in at least j output edge images.

3. These consensus images are compared with the each output image Oj ,

to find the empirical discrepancy measure between consensus and edge

image.

Discrepancy measure = Vjk = D(Oj, Ck) (3.1)

4. The discrepancy measure corresponding to each consensus image are

processed using merging method to find its global consensus value GK .

5. Finally an optimization operation is done to compute the optimum con-

sensus level that optimize the N consensus values.

The optimum vote or consensus level is chosen for reference image using

two novel approaches namely: Minimean and Minimax [2].

3.2.4 Minimean Method

The optimum consensus level can be determined by taking the minimum

value of the mean of kth where kε(1 . . . N) level consensus and output of each

of the methods. It can be expressed as follows,


Gk =1

N

N∑i=1

{Vj,k (3.2)

koptimum,min(Gk)ε(Gk) (3.3)

3.2.5 MiniMax method

The minimum value of the maximum of Kth consensus level (jε{1, ..., N})and output of each of the methods are used to select the optimum position

for ground truth image. Which is expressed as follows,

Gk = max{Vj,k|1 ≤ j ≤ N} (3.4)

koptimum,min(Gk)ε(Gk) (3.5)

The output of each method is shown in figure 3.3. The choice of best reference

image using these two (minimean and minimax) methods is an essential step

for performance evaluation.

3.3 Performance measures

The edge detection algorithms are based on different criteria thus, they are

sensitive to distinct edges. To judge the efficacy of the edge detection methods

Canny proposed three criteria as discussed in chapter 2. Therefore, perfor-

mance measures are required to find an edge detector which satisfies these

criteria. Four different performance indices have been considered here to

server this purpose.

• Edge Miss match Error (EMM)

• figure Of Merit(FOM)

• F-measures

• Precision-Recall curve (PR curve)


Figure 3.1: Frame work for generation of consensus ground truth

(a)

Figure 3.2: Input image


(a) (b)

Figure 3.3: Consensus ground truth by using(a) minimean, (b) minimax method

All the selected metrics require reference image for evaluation, which is

generated using discussed consensus approach (see Section 3.2.3 for more

details).

3.3.1 Edge Missmatch Error (EMM)

Edge Missmatch Error (EMM) finds the measure of change in the location

of edge pixels in the detected edge image with respect to the reference edge

truth image.

EMM = 1 − CE

CE +W [∑

kε(EO) δ(K) + α[∑

lε(ET ) F (l)]](3.6)

Here,

� CE (Common Edges) - The number of common edge pixels between

reference ground truth image and edge image.

� EO (Excess Original Edge) - The number of excess edge pixels in refer-

ence ground truth image which are not present in edge image.

� ET (Excess Thresholded Edge ) - The number of excess edge pixels in

edge image which are not present in reference ground truth image.


� δ(K)- Distance function

δ(K) =

⎧⎨⎩|dK |; f |dk| ≤ maxdist

Dmax; otherwise(3.7)

� dk- The Euclidean distance between the kth edge pixel to the comple-

mentary edge pixel within maxdist.

� maxdist = 0.025 N

� N =√Nrow ∗Ncoloumn

� Dmax = 0.1N

� w = 10N

� α = scalingfactor(2)

3.3.2 figure Of Merit(FOM)

Pratts figure of Merit (FOM) is appropriate measure to identify the false

positive error. This measure lacks in are having the disadvantage as there is

no proper theoretical justification [19] and it is also not sensitive to a false

negative type error. However this index provides discrepancy measure for

edge localization, estimating minimum distance from expected edge point. It

is normalized in between 0 and 1, which is formulated as follows:

F =1

max{Iref , Iedge}Iedge∑i=1

1

1 + αd2(i)(3.8)

Here

� Iref -The no of edge points in reference ground truth image.

� Iedge -The no of edge points in detected edge image.

� α -Scaling constant=19


� d - Separation distance between the edge point in the reference ground

truth image and detected edge image.

Eq..eq:ch3:Performance evaluation indicates the separation distance ‘d’ is

inversely proportional to FOM. For smeared edge the displacement of pixels

from its original position increase which causes an increase in separation dis-

tance and the corresponding value of FOM decrease. Thus, the edge detectors

with a higher value of FOM are well localized.

3.3.3 F-measure

F-measure or F-score or F1metric is the weighted harmonic mean of precision

and recall. It is used to indicate the classification accuracy.

F −measure = 2× Precision×Recall

Precision+Recall(3.9)

Here ,Precision or sensitivity or True Positive Rate is the ratio of the no of

pixel which are defined as edge pixel in both reference and detected image to

the total no of edge pixel in detected image.

Precision =TP

TP + FP(3.10)

Recall - on the other hand it is the ratio between the number of pixel which

are defined as edge pixel in both reference and detected image to the total

number of edge pixel in reference image.

Recall =TP

TP + FN(3.11)

The confusion matrix for the F-Measure as shown in figure 3.4, yields detector

performance.

3.3.4 Precision Recall (PR)Curve

Precision Recall (PR) curve represents the relationship between the recall

and sensitivity for a large dataset/database. Binary decision based dataset


Figure 3.4: Confusion matrix

may be well classified using both Receiver Operating Curve (ROC) and/or

Precision Recall (PR). However literature suggests that PR curve more ef-

fectively classify the skewed dataset, i.e. data with negative counts much

more than positive counts [14]. Thus a large change in false positive can

raise a very small change in False Positive Rate (FPR). Unlike ROC curve,

Precision Recall curve compares false positive with true positive instead of

true negative. This includes a large number of negative examples in the algo-

rithm’s performance. Therefore, PR curve would provide better evaluation

for different edge detector than ROC curve.

3.4 Discussion

This chapter includes different type of approaches for the ground truth gen-

eration. It also covers application and limitations of these approaches. The

ground truth edge map, thus obtained from consensus method is used for per-

formance evaluation of different edge detectors using discussed quantitative

evaluation metrics.

Chapter 4

Real-time Canny Edge Detection System

Design

4.1 Introduction

This chapter describes the design of a real time image processing for Canny

edge detector system which make use of the test bench developed in chapter

5. The design and simulation was done for a single frame. The targeted

system should acquire frames from an acquisition system and should detect

edges in them.

4.2 Architecture Selection/Parallel Algorithm Development

4.2.1 Architecture Selection on FPGA

In the FPGA based circuit design, estimation of different system performance

parameters is required. The first step is the selection of the FPGA system

architecture. A Canny based edge detection algorithm is based on sequential

operation but it can also be designed by considerable amount of parallelism in

it. Each module of canny can be implemented in parallel. Thus to effectively

utilize this parallelism, an architecture which is completely parallel in nature

will be selected. A standalone FPGA architecture is the best choice for this

32

CHAPTER 4. REAL-TIME CANNY EDGE DETECTION SYSTEM DESIGN 33

design, as it is completely parallel.

4.2.2 FPGA Computational Architecture Selection

The next step is the selection of FPGA memory (computational) architecture.

This design involves buffers at input and output end, for storing the incoming

input image pixel values and processed output values. Thus the incoming

pixels can not be processed on the fly. The best method of accessing data

from a buffer is random access processing. Path between the input and output

buffer are continuous at the same time. Therefore, there is no need of storing

intermittently. Hence, stream processing can be used in this section. Thus

the whole design is a combination of random access processing and stream

processing.

4.2.3 Selection of FPGA Mapping Techniques

The FPGA mapping techniques is used for achieving desired system perfor-

mance. In this design, pipe-lining and caching has been used for accelerating

the overall system performance without loss of pixels. A pipeline is im-

plemented to accelerate the processing of the pixels. The Gaussian mask,

SOBEL mask, non maxima suppression is implemented in pipe-line. Each

pipe line includes three stages. The result will be stored to the output cache

memory in the third stage. While the current pixel is being stored to output

cache, the result of the next pixel will be calculated simultaneously in the

second stage of the pipe. At the same time, a third pixel will be fetched in

first stage of the pipe. This pipelining of data helps the system to process

many pixel at the same time.

Selection of Cache Memory

Caching is used to improve system latency. In this process a four pixel wide

cache is applied to avoid frequent reading of data from the main memory. To


find out the result at the central pixel, nine neighboring pixels (3 rows of 3

pixels) are needed . But as normally the size of cache memory is defined in

powers of two so a 4 pixel wide cache memory is setup to store one row. Three

such memories are designed to store three neighboring rows i.e. previous row,

current row and the next row. In particular caching is implemented by row

buffering technique.

4.3 Over all architecture

The over all architecture of the Canny edge detection system is as described

in chapter 2. The architecture is divided into four parts.

• Smoothing

• Gradient calculation

• Non Maxima Suppression

• Hysteresis Thresholding

4.3.1 Smoothing

The entire circuit of smoothing operation can be divided into four parts [20].

• Buffering

• Indexing

• Caching

• Pipeline

The data from the MATLAB output hex file will be buffered in the internal

frame buffer, with one pixel in every clock pulse. This data will be then

routed to cache memory through appropriate control signals. To calculate a

smoothed pixel, eight neighboring pixels has to be fetched from buffer. Four


pixels will be fetched at a time from the buffer and will be stored in a four

byte cache. Four pixels of previous row, present row and next row will be

buffered in to three different cache memories, with each memory has a size

of four bytes. At the end of first row of buffer, the test bench will generate a

horizontal synchronous pulse, it will disable the data valid signal to represent

the data is invalid. After the completion of three rows this will enable the

data path between buffer and the cache memory corresponding to present

row (present row cache). In a similar way data will flow from buffer to the

cache memories corresponding to current and next rows. The addressing for

the different row is as shown in figure 4.4. When the three rows are filled, by

using shifting operation pipeline acquire data. The gaussian mask is applied

in pipelining as in figure 4.5a-4.6b. Path from pipeline to the output cache

memory will not be enabled unless the input row cache memories are full.

The result will be stored in the output gaussian buffer.

Figure 4.1: Architecture for Gaussian smoothing

4.3.2 Gradient and magnitude calculation

As explained in Chapter 2 the next step of Canny is gradient and magnitude

calculation. For this Sobel mask in x and y direction is implemented in pipe

line [21] in similar way as explained in above section for Gaussian mask. The

architecture for these calculation is as show in figure 2.3. Data from Gaussian

buffer is divided into three cache memories, and shifted towards pipe with


(a) (b)

Figure 4.2: (a) Previous Row buffering, (b) Current Row buffering

(a) (b)

Figure 4.3: (a) Next Row buffering, (b) Result Row buffering

Figure 4.4: Indexing Circuit

increase in each clock. After the Sobel operation in both the direction in

pipeline the result gradient in x and y direction is used for gradient magnitude

and direction calculation. The steps for magnitude and angle calculation is

included with the architecture of non maxima suppression as explained in

next section.


(a) (b)

Figure 4.5: Data flow of pipeline in first three clock

(a) (b)

Figure 4.6: Data flow of pipeline in next two clock

Figure 4.7: Architecture of dx and dy calculation

4.3.3 Non-maxima calculation

The architecture for non maxima suppression is in figure ??. The gradient

magnitude and direction is calculated by using dx and dy value in previous

section. For the angle calculation look up table is used. The angle is ap-

proximated to the four predefined gradient direction. Then the comparison


of the current pixel with its two neighborhood along the direction is done. If

the magnitude of the current pixel is less than any of the magnitude of its

neighbor along the direction replace the current pixel with zero i.e. no edge.

Else the current pixel is marked as edge point.

Figure 4.8: Architecture of Non-maxima calculation

4.3.4 Hysteresis calculation

In hysteresis thresholding we choose two threshold values as discussed in

chapter 2. In the output buffer of previous step we apply these two thresholds

by using comparator as shown in figure fig:ch5:Hysteresiscalculation1. These

threshold values segregate the buffer into two image f1(x, y) and f2(x, y) pixel

is results in two image. With the use of consecutive OR and AND gate as,

false edge points are removed by using following steps

• If the central pixel in f1(x, y) is 1 then it is directly taken as a true edge

pixel.

• If the central pixel in f1(x, y) is 0, and if any of the neighbor in f1(x, y)

of the current pixel is 1 and central pixel in f2(x, y) is 1, then it is taken


as a true edge pixel, else discard the pixel.

Figure 4.9: Architecture of Hysteresis calculation

4.4 Discussion

This chapter include the architecture design of Canny edge detection algo-

rithm for including considerable amount of parallelism in it . For the design of

each section buffering, caching and pipeline processing is used. As in Canny

every step is dependent on the previous step result. In this design each mod-

ule is working in parallel after some initial delay. These parallelism in design

accelerate the overall architecture speed.

Chapter 5

Design of a VHDL Test-bench for Canny

edge detection

5.1 Introduction

A real-time system process information and generate a response within a

specified time limit, else risk severe consequences, including failure. In image

processing the real-time system must process an input image to produce

certain output image such that it preserves desired features for down stream

applications within a certain time limit. To gain maximum performance,

these image processing systems are designed using parallel processor and the

architectures are implemented in various hardware platforms.

5.2 Need for the Test-Bench

For hardware implementation of any design problem, initially it must be

validated and verified in software platform. Once hardware is designed it will

be difficult and time consuming task to fix any problem. Hence in software

we need to develop an architecture for simulation of real-time systems. In

this thesis, we have developed a test bench and simulated it in VHDL for

edge detection of an image using Canny’s method. The reported architecture

40

CHAPTER 5. DESIGN OF A VHDL TEST-BENCH FOR CANNY EDGE DETECTION 41

may serve as the prototype for its hardware implementation in FPGA.

5.3 Model for an Image Processing System

framework for the representation of real time image processing system is given

in figure ??. Initially image is acquired from the sensors of camera unit.The

preprocessing is achieved by IP core using sequential processors like MC and

DSP. Preprocessing steps may also includes image filtering, smoothing of

image for noise reduction and color to gray conversion. The image frames thus

stored will be accessed by a prime image processor, based on applications,

which may be an FPGA-based parallel processor, for further processing. In

this processor any image processing algorithm can be implemented. After

the completion of assigned task output will be stored in frame buffer. This

buffer and display are connected to same IP core, from which data can be

sent to any output device.

Figure 5.1: Model of Image Processing System

5.4 Image Representation

As the Fig.(5.2) indicates the composite image signal contains image intensity

values as well as certain synchronization signals. A horizontal and vertical

synchronous pulses are used to indicate end of row and end of the image,

respectively. Moreover any incoming data is validated using a data valid

signal. This can be checked using a high pulse.


Figure 5.2: Image Representation in analog form

Figure 5.3: Image Representation in digital form

5.5 Image Processing Test Bench

The image processing test bench must be able to read an input image file,

generate clock pulses for various operations, generate synchronization pulses

and make the image accessible to the main processor where necessary oper-

ation is performed on the image. Since images cannot be accessed directly

in VHDL, we need to generate a text file from external program ( MATLAB

is used here) which can represent the image in readable form to VHDL. The

same external MATLAB program is used for the generation of output image

from the output hex file, generated in VHDL. The overall process is shown

in block diagram with three important modules of the test bench is as shown

in figure 5.4


Figure 5.4: Block diagram of a image processing test bench

5.5.1 Image to Hex-Image Converter

Since VHDL cannot access the images directly, this MATLAB program will

convert the incoming image frame in to hex format image file where each

intensity value will be written in hexadecimal format.

Hex-Image File

This image can be accessed by writing the intensity values of the image into

a text file. The text file can be generated by an external program in MAT-

LAB. Each pixel value or the intensity value of the image will be converted

and written in to hexadecimal format. It will be stored as a sequence of 2

continuous characters.

For example the intensity value 8 will be converted into hex value stored

as 08. Similarly the intensity value 255 will be stored in hex format as FF. All

the intensity values from 0 to 255 is converted to their respective Hex-values,

and coded between 00 and FF. A ‘, character is written at the end of each

row. A ‘* character will be placed at the end of each image frame. This

conversion and coding scheme and finally writing down to a text file is shown

in Fig.(5.5). The image file with hex values of pixels is generated for a 256 x

256 Lena image.


Figure 5.5: Coding of image into a hex image file

5.5.2 VHDL Camera Module

This module is a program written in VHDL. These programs were written and

developed in ModelSim 10.4a platform. This module takes the image pixel

values from the hex file generated. The hexadecimal values will be converted

into standard logic vector of 8 bit length. In addition, it generates clock

pulses for operation of the FPGA processor and display driver. It generates

clock pulse of 100ns. After every 100ns the clock pulse will change its state.

Whenever the rising edge of clock occurs, the program reads a character from

input hex file. It checks the character then. If it is a ‘,’, then a horizontal

synchronous pulse is generated and if the character is ‘*’, then a vertical

synchronous pulse is generated. Each of the horizontal synchronous pulse

vertical synchronous pulse are of one clock duration. If the encountered

character is a hexadecimal number then a ‘data valid’ signal is generated

and it will be converted to standard logic format. Single bit of hexadecimal

number will be converted to 4 bit length standard logic vector. Thus for 2

bits of hexadecimal number, this module generates 8 bit length standard logic

signal representing the intensity value of the image pixel. The flow chart of

the camera module is shown in Fig.(5.6).

5.5.3 Output Display Module

The Display of output image can be attained by writing the output image

values into a text file. This text file can be read by an external MATLAB


Figure 5.6: Algorithm for generating composite image signal from hex file

program. It generates the output image from the text file and thus displays

the output.

5.5.4 Output Signals from Test Bench

The main output signals present in camera module of VHDL are as follows:

• A clock pulse

• Horizontal synchronization pulse

• Vertical synchronization pulse

• Data valid signal

The simulation was performed in ModelSim 10.4a and the generated results

are shown in Fig.(5.7).

Clock Pulse

The clock pulse is designed to change its state after every 100ns. Depending

on the application the clock time period can be modified. By default clock


Figure 5.7: Simulation results

pulse is designed to toggle its state in every 100ns. As the application de-

mands, this value can be modified to meet the specifications. All the signals

in camera module, Edge main module and display module and other events

will be synchronized with the clock pulse. The Fig.(5.7) shows the generated

clock pulse in red color.

Horizontal Synchronous Pulse

Whenever there is an end of the row a horizontal synchronous pulse will be

generated. It is of one clock pulse duration. Total number of horizontal

synchronous pulse generated will be equal to the number of rows in our input

image. The signal is shown in blue color in the waveform in Fig.(5.7).

Vertical Synchronous Pulse

Whenever VHDL detects that there is an end of the frame a vertical syn-

chronous pulse will be generated. It is also of one clock pulse duration. Total

number of vertical synchronous pulse generated will be equal to the total

number of frames. The signal is shown in green color in the waveform in

Fig.(5.7).

Data Signal

This is an image data signal shown in pink color. The data signal is present in

standard logic vector format, and it will be sent to the image processor. The


data signal is of length equals to 8 bit Fig.(5.7). The camera module changes

the data from hexadecimal to standard logic format and display module will

get same data signal. After that it will be converted in to hexadecimal format

for writing into output file.

Data Valid Signal

The status of the data signal is informed by the data valid signal. It goes low

if an invalid data is detected otherwise for a valid data signal it remains high.

Whenever a horizontal and vertical synchronous pulse are high,the data valid

signal signal goes low. That means on the occurrence of a ‘,’ or a ‘*’ data

valid signal is low. Signal is shown in yellow color in the Fig.(5.7).

5.6 Discussion

Before any hardware implementation it is essential to validate and verify any

real time model in simulation platform. In this chapter we discuss about

the implementation procedure for image analysis in VHDL platform. The

developed test bench can be simulated for real-time image acquisition system.

Chapter 6

Results and Discussion

In this thesis, we have compared various edge detection algorithm. Here,

three different categories of edge detection techniques are considered that

includes Sobel, Roberts, Canny, Prewitt, Phase congruency and LOG oper-

ator (as discussed in chapter 2). For the comparison, different performance

indices such as: edge miss match error (EMM), figure of merit (FOM), F-

measure and precision recall curve (PR) curve is used. These performance

measures require reference image for evaluation. Consensus of different edge

detectors is used for automatic generation of ground truth image which takes

two merging method, minimean and minimax.

6.1 Results

6.1.1 Experimental setup

In this context four different databases with more than 1500 images of dif-

ferent human faces, natural scenes, buildings and objects containing differ-

ent textural characteristic, with various percentage of homogeneous regions,

edges, and details are considered for the experiment. More detail about each

database are given in Table.6.1. For unification purpose, all the images in

these databases are cropped to size 256× 256 pixels.

48

CHAPTER 6. RESULTS AND DISCUSSION 49

Table 6.1: Database used for experimental validation

DatabaseOriginalImage Type

No. ofImages

ImageResolution

Other Specification

Airplane andLeaves image

Airplane andLeaves image

1260 602× 4021074 Airplane and186 Leaves image

TID 2008Database

Natural andArtificial Images

25 512× 38424 Natural images and1 Artificial image

Zurich ObjectDatabase

Object Images 381 320× 240115 Building and269 Object Images

6.1.2 Consensus based reference image generation

As discussed in chapter 3 for the comparison in various edge detectors there

is a requirement of reference image. The reference edge map as shown in

figure 6.1 is generated considering minimean and minimax method, respec-

tively. MATLAB based Graphical user interface(GUI) as shown in figure was

developed as a part of this work for quantitative evaluation of edge detection.

This GUI has two options, we can either choose one image or multiple images

at a time. For single image it generate the consensus reference image, edge

map of all detectors and three performance measure for comparative evalu-

ation. We also recorded performance measures for different image databases

using multiple image option in GUI. These measures are used for quantitative

comparison.

6.1.3 Performance measure on different data base

Initially all the considered metrics are normalized between [0,1], where 0 in-

dicates the reference edge map and the test edge map are same while 1 repre-

sents otherwise. The overall performance measure for each image database is

calculated using Average Performance index (API) for comparative analysis.

Which is defined as follows:

API =EMM + F −measure+ FOM

3(6.1)


Ground trutth image

(a)

Ground trutth image

(b)

Figure 6.1: Consensus based reference image using, (a) minimean and, (b) minimax merging method

Figure 6.2: MATLAB based GUI for edge detection evaluation.

Performance measure results for each data base is shown in Table. 6.2-6.9.

Table 6.2: Performance measure for Caltech airplane database with minimean merging

Sobel Prewitt Canny Roberts LOG Phase Congruency

F-measure 0.4828 0.4815 0.4813 0.5766 0.4024 0.7593

EMM 0.0481 0.0476 0.0145 0.0523 0.0031 0.0160

FOM 0.5938 0.5926 0.3075 0.6271 0.3483 0.7826

API 0.3749 0.3739 0.2677 0.4186 0.2512 0.5193


Table 6.3: Performance measure for Caltech leaves datasbase with minimean merging for referenceimage generation


F-measure 0.5378 0.5389 0.4485 0.5884 0.4476 0.6636

EMM 0.0714 0.0902 0.0729 0.0581 0.0077 0.1185

FOM 0.6468 0.6493 0.2681 0.6436 0.3888 0.7096

API 0.4186 0.4261 0.2631 0.4300 0.2813 0.4972

Table 6.4: Performance measure for TID2008 with minimean merging for reference image generation


F-measure 0.5194 0.5191 0.5202 0.6599 0.3640 0.7457

EMM 0.0277 0.0139 0.0137 0.0563 0.0129 0.0322

FOM 0.6442 0.6471 0.1749 0.7191 0.2365 0.7743

API 0.3971 0.3933 0.1749 0.719 0.2365 0.7743

Table 6.5: Performance measure for Zurich Object Database with minimean merging for referenceimage generation


F-measure 0.4250 0.4238 0.4731 0.5212 0.4330 0.6370

EMM 0.0096 0.0071 0.0129 0.0322 0.0131 0.0037

FOM 0.4988 0.4994 0.2767 0.5147 0.3261 0.6268

API 0.3111 0.3101 0.2542 0.3560 0.2574 0.4225

Table 6.6: Performance measure for Caltech airplane datasbase with minimax merging for referenceimage generation


F-measure 0.5014 0.4998 0.4442 0.5774 0.4835 0.7676

EMM 0.0006 0.00066 0.0020 0.0009 0.00103 0.0008

FOM 0.5833 0.5821 0.3891 0.6201 0.4312 0.7886

API 0.3617 0.3608 0.2784 0.3994 0.3052 0.5190

Table 6.7: Performance measure for Zurich Object Database with minimax merging for referenceimage generation


F-measure 0.5904 0.5910 0.3449 0.6004 0.4805 0.7107

EMM 0.0012 0.0011 0.0040 0.0010 0.0010 0.00115

FOM 0.7386 0.7392 0.4924 0.7444 0.5868 0.809

API 0.4433 0.4437 0.2804 0.4496 0.3561 0.5069


Table 6.8: Performance measure for Caltech leaves database with minimax merging for referenceimage generation


F-measure 0.5422 0.5430 0.4315 0.5816 0.5125 0.6647

EMM 0.0110 0.0110 0.0042 0.0085 0.0077 0.0056

FOM 0.6316 0.6341 0.3551 0.6246 0.4541 0.6928

API 0.3949 0.3960 0.2635 0.4049 0.3247 0.4543

Table 6.9: Performance measure for TID2008 database with minimax merging for reference imagegeneration


F-measure 0.4294 0.4267 0.6151 0.5933 0.5619 0.6689

EMM 0.00061013 0.000666 0.0018137 0.00079491 0.00223 0.0077

FOM 0.3493 0.3476 0.2519 0.4301 0.2561 0.5553

API 0.2597 0.2583 0.2896 0.3413 0.2734 0.4106

Table 6.10: AUC calculation for Precision Recall curve using minimean method

Caltechairplane datasbase

CaltechLeaves dataset

TID2008Zurich

Object Database

Sobel 0.7178 0.7198 0.5898 0.6787

Prewitt 0.7227 0.7072 0.5506 0.6817

Robert 0.5694 0.6149 0.5190 0.6061

LOG 0.5982 0.6492 0.5031 0.6134

Phase Congruency 0.4532 0.5213 0.4482 0.5189

Canny 0.7368 0.7371 0.6214 0.6832

6.1.4 Precision Recall curve

Precision recall (PR) curve is a graphical approach, which represent sensitiv-

ity verses precision. PR curve for minimean and minimax method is as shown

in figure 6.3 and 6.4. Area under the curve is also calculated which is shown

in Table 6.11 and 6.11. AUC lies between 0 and 1 where, 0 is considered as

worst and 1 is as best value. If the PR curve of any edge detector is greater

than 0.5 then it is considered as a better edge detector. More the AUC more

the performance of considered detector.


0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Recall

Prec

isio

n

Sobel Prewitt Robert LOG Phase Congruency Canny

(a)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

Recall

Prec

isio

n


(b)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Recall

Prec

isio

n


(c)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Recall

Prec

isio

n

Sobel Canny Prewitt Robert LOG Phase Congruency

(d)

Figure 6.3: Comparison of different edge detector for minimean method using PR curve on(a)Caltech airplane database[——ref—–], (b)Caltech leaves database,(c)TID2008, (d)Zurich Ob-ject Database

6.1.5 Edge detection in VHDL

From the results of Performance measure and PR curve for minimean and

minimax on each database, we found that Canny edge detector is a consistent

operator for edge detection. Thus for implementation of canny edge detector

an architecture is developed in VHDL for hardware realization in FPGA. The


0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Recall

Prec

isio

n Sobel Prewitt Robert LOG Phase Congruency Canny

(a)

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Recall

Prec

isio

n

Sobel Prewitt Robert LoG PhaseCong Canny

(b)

0 0.2 0.4 0.6 0.8 1−0.2

0

0.2

0.4

0.6

0.8

1

Recall

Prec

isio

n


(c)

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Recall

Prec

isio

n

Sobel Prewitt Robert LOG Phase congruency Canny

(d)

Figure 6.4: Comparison of different edge detector for minimax method using PR curve on (a)Caltechairplane datasbase, (b)Caltech leaves datasbase,(c)TID2008, (d)Zurich Object Database

developed architecture adopts Sobel’s mask for gradient magnitude and angle

calculation for Canny edge detector. For the simulation, as in VHDL we can

not read image directly thus we have used ModeSim PE Student edition 10.4a

along with MATLAB 2012 is used to read an image in VHDL for simulation

of Sobel’s architecture [?]. MATLAB converts the image file format to hex

file, that serves as input in VHDL. The processed image (in hex format) from

VHDL is converted back to binary image using MATLAB. Initial attempt for

edge detection using Sobel’s operator is simulated using VDHL. The result

as shown in figure 6.6, indicates the potential of parallel processing in image


Table 6.11: AUC calculation for Precision Recall curve using minimax method

Caltechairplane datasbase

CaltechLeaves dataset

TID2008Zurich

Object Database

Sobel 0.6828 0.6595 0.5842 0.5912

Prewitt 0.6824 0.6703 0.5741 0.5298

Robert 0.5972 0.6848 0.5143 0.6215

LOG 0.5123 0.5660 0.5283 0.6878

Phase Congruency 0.5731 0.5210 0.4548 0.6961

Canny 0.7532 0.7193 0.5083 0.7105

analysis.

Figure 6.5: Input image

(a) (b)

Figure 6.6: Ege detction by Sobel method, (a) MATLAB output, (b)VHDL output image

6.2 Discussion

Experimental setup is created as shown in Table 6.1. The results indicate

that the performance of edge detection algorithm varies with the image i.e.


behavior of detector depends totally on selection of images. Results also

illustrate that point edges are more prominent and easily distinguishable.

The images with less textural information provides better edge map. Unlike,

we have considered both minimean and minimax methods for edge evaluation.

Since Canny uses smoothing for noise removal, nonmaxima suppression for

edge localization and hysteresis for false edge extraction, it is more robust

for different type of images. The architecture for Canny edge detector uses

Sobel mask for gradient magnitude calculation in VHDL. The result for Sobel

operator illustrate that the time efficient processing of FPGA based parallel

processor.

Chapter 7

Conclusion and Future Work

7.1 Conclusion

In this thesis, we have studied different types of edge detection techniques

and evaluated these methods using four performance measures. The need of

reference edge map for quantitative evaluation using EMM, FOM, F-measure

and PR curve motivates to generate reference image using consensus of dif-

ferent edge detectors. The minimean and minimax methods are considered

for automatic generation of ground truth edge map using optimum vote. The

experimental results on various images containing a wide range of natural im-

ages of varying illumination, contrast and textural details yield the potential

of Canny edge detector over other methods.

Due to the ever increasing demand for high speed and time critical tasks

in many image processing applications, an efficient hardware architecture for

Canny edge detector is implemented in VHDL. The studied implementation

technique adopts parallel architecture of Field Programmable Gate Array

(FPGA) to accelerate the process of edge detection via. Canny’s algorithm.

We have simulated the considered architecture in Modelsim 10.4a student

edition to demonstrate the potential of parallel processing for edge detection.

The analysis and implementation technique may encourage and serve as a

57

CHAPTER 7. CONCLUSION AND FUTURE WORK 58

basis building block for several complex computer vision applications.

7.2 Future work

The performance of studied algorithm for automatic reference edge map gen-

eration using consensus of different edge detector may be improved by includ-

ing more edge detection algorithms. Moreover the process of parallel opera-

tion for Canny edge detector may be accelerated. The choice of different edge

detection algorithms and the hardware architecture for its implementation is

left as future scope of this thesis.

Bibliography

[1] M. Sezgin and B. Sankur, “Selection of thresholding methods for nondestructive testing applications,”

in Image Processing, 2001. Proceedings. 2001 International Conference on, vol. 3. IEEE, 2001, pp.

764–767.

[2] N. L. Fernandez-Garcıa, A. Carmona-Poyato, R. Medina-Carnicer, and F. J. Madrid-Cuevas, “Auto-

matic generation of consensus ground truth for the comparison of edge detection techniques,” Image

and Vision Computing, vol. 26, no. 4, pp. 496–511, 2008.

[3] S. M, “Development of an fpga based image processing intellectual property core,” M.Tech dissertation,

NIT Rourkela, May 2014.

[4] D. Ziou, S. Tabbone et al., “Edge detection techniques-an overview,” Pattern Recognition and Image

Analysis C/C of Raspoznavaniye Obrazov I Analiz Izobrazhenii, vol. 8, pp. 537–559, 1998.

[5] R. C. Gonzalez and R. E. Woods, “Digital image processing,” 2002.

[6] L. G. Roberts, “Machine perception of three-dimensional soups,” Ph.D. dissertation, Massachusetts

Institute of Technology, 1963.

[7] M. A. Oskoei and H. Hu, “A survey on edge detection methods,” University of Essex, UK, 2010.

[8] R. O. Duda, P. E. Hart et al., Pattern classification and scene analysis. Wiley New York, 1973, vol. 3.

[9] M. C. Morrone, J. Ross, D. C. Burr, and R. Owens, “Mach bands are phase dependent,” Nature, vol.

324, no. 6094, pp. 250–253, 1986.

[10] R. Owens, S. Venkatesh, and J. Ross, “Edge detection is a projection,” Pattern Recognition Letters,

vol. 9, no. 4, pp. 233–244, 1989.

[11] P. Kovesi, “Image features from phase congruency,” Videre: Journal of computer vision research, vol. 1,

no. 3, pp. 1–26, 1999.

[12] D. Marr and E. Hildreth, “Theory of edge detection,” Proceedings of the Royal Society of London B:

Biological Sciences, vol. 207, no. 1167, pp. 187–217, 1980.

[13] J. Canny, “A computational approach to edge detection,” Pattern Analysis and Machine Intelligence,

IEEE Transactions on, no. 6, pp. 679–698, 1986.

59

BIBLIOGRAPHY 60

[14] T. Saito and M. Rehmsmeier, “The precision-recall plot is more informative than the roc plot when

evaluating binary classifiers on imbalanced datasets,” PloS one, vol. 10, no. 3, p. e0118432, 2015.

[15] D. J. Bryant and D. W. Bouldin, “Evaluation of edge operators using relative and absolute grading,”

in Conference on Pattern Recognition and Image Processing, vol. 1, 1979, pp. 138–145.

[16] K. Bowyer, C. Kranenburg, and S. Dougherty, “Edge detector evaluation using empirical roc curves,”

in Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference on., vol. 1.

IEEE, 1999.

[17] Y. Yitzhaky and E. Peli, “A method for objective edge detection evaluation and detector parameter

selection,” Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 25, no. 8, pp. 1027–

1033, 2003.

[18] A. J. Baddeley, “An error metric for binary images,” Robust computer vision, vol. 5978, 1992.

[19] L. Ding and A. Goshtasby, “On the canny edge detector,” Pattern Recognition, vol. 34, no. 3, pp.

721–725, 2001.

[20] D. G. Bailey, Design for embedded image processing on FPGAs. John Wiley & Sons, 2011.

[21] P. J. Ashenden, “Digital design. an embedded system approach using vhdl,” 2008.

Authors Biography

Nidhi Panda was born to Mr. Devendra Panda and Mrs. Madhu Panda

on 15th February, 1992 at Raigarh, Chhattisgarh, India. She obtained her

Bachelors degree in Electronics and Telecommunication Engineering from

Disha Institute of Management and Technology, Raipur, Chhattisgarh in

2013. She joined the Department of Electrical Engineering, National Institute

of Technology, Rourkela in July 2014 as an Institute Scholar to pursue Master

of Technology.

61

analysis of edge detection technique for hardware...

Documents